On 4/06/2018 11:19 PM, Vibrator ! wrote: . . . The only precondition there is that we can apply a force between two inertias, which nonetheless only accelerates one of them. This I suggest is your problem. If you apply a force between two masses or inertias, then one must accelerate in the opposite direction to the other (Newton's first law). If one of them is massive enough (eg make it the earth), then only the light one is accelerated by any measurable amount (but the tiny acceleration of the heavy one ensures that momentum is conserved).
You could apply a force between two equal inertias so that one accelerates forward and the other accelerates backwards, and then bounce one of them off a wall fixed to the earth say. Now you would have them both moving in the same direction and with the same speed. But their total kinetic energy would be equal to that put in during the acceleration phase (the bounce being elastic and conservative). So each would contain say 0.5 joules of energy for a total of one joule put in by the initial acceleration impulse. Let's call this square one. At this stage you could then apply the same accelerating impulse as the first time between the two inertias (which are now both travelling along together) and the speed of one would double, while the other would become stationary. Here the kinetic energy of one has gone up by a factor of 4 (due to v^2) to become 2 joules while the energy of the other has gone down to zero - the total being the 2 joules that have been put in by the two accelerations (so no gain). Call this square two. Then we inelastically collide them (as by a length of string being pulled taut), equalising their velocity, and keep repeating that process, whilst monitoring input / output efficiency (how much energy we've spent vs how much we have). As you note, inelastic collisions waste kinetic energy by turning it into heat. So joining the stationary mass to the travelling mass inelastically with a piece of string will produce a combined speed which is just the same as the speed of both masses before applying the second impulse (from conservation of momentum). So the entire effect of the second impulse will have been undone taking us back to square one. I see no way to progress beyond square two that does not simply take us back to square one?
